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This is the second part of our new column on risk and uncertainty. David Spiegelhalter, Winton Professor for the Public Understanding of Risk at the University of Cambridge, continues examining league tables using the Premier League as an example. Find out just how much — or how little — these simple rankings can tell you.

According to Darwin, natural selection is the driving force of evolution. It's a beautifully simple idea, but given the thousands of years that are involved, nobody has ever seen it in action. So how can we tell whether or not natural selection occurs and which of our traits are a result of it? In this article Charlotte Mulcare uses milk to show how maths and stats can provide genetic
answers.

Next year is a great one for biology. Not only will we celebrate 150 years since the publication of On the origin of species, but also 200 years since the birth of its author, Charles Darwin. At the heart of Darwin's theory of evolution lies a beautifully simple mathematical object: the evolutionary tree. In this article we look at how maths is used to reconstruct and understand it.

Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there any tilings based on fiveness? Craig Kaplan takes us through the five-fold tiling problem and uncovers some interesting designs in the process.

In the fourth and final part of our series celebrating 300 years since Leonhard Euler's birth, we let Euler speak for himself. Chris Sangwin takes us through excerpts of Euler's algebra text book and finds that modern teaching could have something to learn from Euler's methods.

League tables are controversial and for good reason. Few things are simple enough to be measured by a single outcome like, for example, the number of exam passes or successful heart operations. But even if we do accept a single yardstick, we haven't yet reckoned with chance, which by itself can produce apparent patterns to delight any tabloid editor.

Over the last few years the words string theory have nudged their way into public consciousness. It's a theory of everything in which everything's made of strings — or something like that. But why strings? What do they do? Where did the idea come from and why do we need such a theory? David Berman has an equation-free introduction for beginners.